About conceptualization, my understanding is that ancient Greek followers of religious leader Pythagoras realized that this was not only a relationship between length and area, but a formula for irrational numbers. This might be a claim without evidence, and would not be the first time Western education has tried that.
Babylonians had no problem arriving at solutions to square roots, and a lot of their texts are yet undeciphered. If we find that Babylonians ruminated about irrational numbers, too, then we’re talking about a major revision in the history of math. Until then, to me, the concepts in the Greek treatments are more innovative than the practical usage in Babylon.
I think your take is supported if it turns out people have read way too much into the religion around Pythagoras. I think Pythagoras would be surprised to be famous for a proof when he’d rather be famous for musical scale or some weird ritualistic dance or something. In fact, as mathematicians we might be better served by later proofs, which is implied by your other points, I think.
Yes, irrational numbers were a great discovery (including how they were discovered) and the systematic treatment of math in The Elements was a better example of the advancement in approaches to knowledge and thinking. And yes, if the Pythagoreans actually thought that this was a formula for irrational numbers, that would indeed to quite impressive.
Babylonians had no problem arriving at solutions to square roots, and a lot of their texts are yet undeciphered. If we find that Babylonians ruminated about irrational numbers, too, then we’re talking about a major revision in the history of math. Until then, to me, the concepts in the Greek treatments are more innovative than the practical usage in Babylon.
I think your take is supported if it turns out people have read way too much into the religion around Pythagoras. I think Pythagoras would be surprised to be famous for a proof when he’d rather be famous for musical scale or some weird ritualistic dance or something. In fact, as mathematicians we might be better served by later proofs, which is implied by your other points, I think.